I would like to run a ssh tunnel from my n900 whenever I am on 3g.

Will this use extra power? Does the ssh tunnel go into a sleep state, or does it leave an idle connection open?

It depends on the configuration. The configuration files are under /etc/ssh/. And even if its active the power that is going to be used is insignificant unless you are performing scp

I thought I read somewhere that idle connections from the n900 increased battery drain.

You will increase the traffic due to encryption. Also, if you use keep alives for the tunnels, that would further increase traffic. So while it won't affect the power usage directly, given that you would be transmitting and receiving more data and also since the CPU would need to perform encryption and hence stay out of idle for longer, it is likely you would see a reduction in battery life usage. A better idea would be to use QueenBeecon to turn the tunnel on and off when you need it, rather than it being on all the time. Your email traffic is encrypted as it is and most decent widgets such as facebook etc. should be using ssl as well, so you won't gain much by having the ssh tunnel ON when the deivce is unattended.

I guess the most negative impact on battery life would come from keeping the connection open. Closing the connection if not used would save a lot of battery power!

Tunneling wouldn't chew on the CPU that much, the main battery drainer in this case would be the 3G radio, at least during idle connection when only a small amount of data is passed between the tunnel and the N900 - to the radio it doesn't matter if it's 10 bytes or 100 kbytes, it will still have to transmit and thus chew through the battery. How much? Well, somebody would have to test it...